If a signing device chooses nonces on its own, a malicious device could theoretically hide a secret in an otherwise normal-looking signature. Connor Avila proposed two anti-exfil BIP drafts on the Bitcoin-Dev mailing list: have the host contribute randomness and verify it after signing; the drafts cover BIP340 Schnorr, ECDSA, and PSBT fields. Important caveat: these are still drafts. The author says they have not yet undergone a cryptographic audit or been run on real devices; they are not an adopted standard or a ready-to-use protection.
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Sources: Author’s original email https://groups.google.com/g/bitcoindev/c/cB37_jChkEI/m/3paRGQ_IBgAJ; protocol draft https://github.com/AvilaLabs/anti-exfil/blob/main/spec/bip-anti-exfil.md; PSBT draft https://github.com/AvilaLabs/anti-exfil/blob/main/spec/bip-anti-exfil-psbt.md
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